Polarization is a general phenomenon and it is not restricted to the Arikan matrix [1]}. One can replace it by a larger matrix, called polarization kernel, which has better polarization properties, thus obtaining better finite length performance. Polar codes with large kernels were shown to provide an asymptotically optimal scaling exponent [2]}.
Some fundamental limits on the rate of polarization together with various kernel constructions were proposed in [1]}, [4]}, [5]}.
